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This paper investigates the existence of resonance and nonlinear stability of the triangular equilibrium points when both oblate primaries are luminous. The study is carried out near the resonance frequency, satisfying the conditions ω1=ω2,  ω1=2ω2, and ω1=3ω2 in circular cases by the application of Kolmogorov-Arnold-Moser (KAM) theory. The study is carried out for the various values of radiation pressure and oblateness parameters in general. It is noticed that the system experiences resonance at ω1=2ω2,  ω1=3ω2 for different values of radiation pressures and oblateness parameter. The case ω1=ω2 corresponds to the boundary region of the stability for the system. It is found that, except for some values of the radiation pressure, and oblateness parameters and for μ≤μc=0.0385209, the triangular equilibrium points are stable.